Kaplansky’s conjectures
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Datum:
15.04.21
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Referent:
Giles Gardam
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Zeit:
15:45-17:30
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Three conjectures on group rings of torsion-free groups are commonly attributedto Kaplansky, namely the unit, zero divisor and idempotent conjectures. Forexample, the zero divisor conjecture predicts that ifKis a field andGis atorsion-free group, then the group ringK[G]has no zero divisors. I will surveywhat is known about the conjectures, including their relationships to eachother and to other conjectures and group properties, and finish with my recentcounterexample to the unit conjecture.